WASHINGTON (AP) — Mitt Romney laid claim to the fiercely contested Republican presidential nomination Tuesday night with a fistful of primary triumphs, then urged all who struggle in a shaky U.S. economy to “hold on a little longer, a better America begins tonight.”

Eager to turn the political page to the general election, Romney accused President Barack Obama of “false promises and weak leadership.” He declared, “Everywhere I go, Americans are tired of being tired, and many of those who are fortunate enough to have a job are working harder for less.”

The former Massachusetts governor spoke as he swept primaries in Connecticut, Rhode Island, Delaware, Pennsylvania and New York, the first since Rick Santorum conceded the nomination.

“Mitt Romney is going to be the nominee, and I’m going to support the nominee,” the former Pennsylvania senator said on CNN. He added he intended to meet on Wednesday with the winner’s aides.

Romney, speaking to cheering supporters, in New Hampshire, said, “The last few years have been the best Barack Obama can do, but it’s not the best America can do.”

He delivered his remarks to a national television audience as well from the state where he won his first primary of the campaign and one of about a dozen states expected to be battlegrounds in the summer and fall campaign for the White House.

Obama campaigned during the day in two others — North Carolina and Colorado — making the case that, however slowly, the economy is growing stronger.

“Our businesses have added more than 4 million jobs over the past two years, but we all know there’s still too many Americans out there looking for work or trying to find a job that pays enough to cover the bills and make the mortgage,” the president said.

“We still have too many folks in the middle class that are searching for that security that started slipping away years before the recession hit.”

Six months before the election, opinion polls show the economy to be the top issue by far in the race. The same surveys point toward a close contest, with several suggesting a modest advantage for the incumbent.

Obama won the presidency in 2008 in the midst of the worst recession since the Great Depression, and since then economic growth has rebounded slowly and joblessness has receded gradually, although housing prices continue to drop in many areas of the country.

In an indication that Romney was treating the moment Tuesday night as something of an opening of the general election campaign, his speech seemed aimed at the millions of voters — non-conservatives and others — who have yet to pay close attention to the race for the White House.

He blended biographical details, an attack on Obama and the promise of a better future, leaving behind his struggle to reassure conservative voters who have been reluctant to swing behind his candidacy.

“As I look around at the millions of Americans without work, the graduates who can’t get a job, the soldiers who return home to an unemployment line, it breaks my heart,” he said. “This does not have to be. It is the result of failed leadership and of a faulty vision.”

Obama, unchallenged for the Democratic nomination, has a head start in organizing, fundraising and other elements of the campaign.

Already, he and aides are working to depict Romney and Republicans as pursuing new tax breaks for the wealthy while seeking to cut programs that benefit millions of victims of the recession as well as other lower-income Americans.

The president campaigned on two college campuses during the day, pitching his proposal to prevent a scheduled increase in the interest rate on new student loans.

Romney, freed of serious primary competition, announced his own general support for the proposal, even though it appears a GOP-drafted budget in the House envisioned no effort to change the pending increase.

Determined to make up for lost time, Romney has recently accelerated his fundraising, announced the beginning of a process to search for a vice presidential running mate and begun reaping endorsements from party officials who declined to do so in the heat of the primary campaign.

Santorum offered no endorsement in a televised appearance during the evening but said he expected to meet with Romney in the future, adding he would sit down with the former governor’s aides on Wednesday.

In his remarks, Romney spoke dismissively of Obama’s tenure in office.

“Government is at the center of his vision. It dispenses the benefits, borrows what it cannot take and consumes a greater and greater share of the economy,” he said.

He added that if the president’s hard-won health care law is fully installed, “government will continue to control half the economy, and we will have effectively ceased to be a free enterprise society.”

By contrast, he said, “I see an America with a growing middle class, with rising standards of living. I see children even more successful than their parents...”

Romney was eager to leave the nominating campaign behind.

“After 43 primaries and caucuses, many long days and not a few long nights, I can say with confidence — and gratitude — that you have given me a great honor and solemn responsibility,” he said.

Romney posed a series of rhetorical questions designed to lead voters to his side.

“Is it easier to make ends meet? Is it earlier to sell your home or buy a new one? Have you saved what you needed for retirement?” he asked.

“Are you making more in your job? Do you have a better chance to get a better job? Do you pay less at the pump?”

At each question, his partisan audience shouted, “No.”

The nominating campaign that still had some loose ends, including the pursuit of national convention delegates.

Romney is still hundreds of delegates shy of a nominating majority, although he is far ahead of his most persistent rivals. There were 209 at stake in Tuesday’s primaries, and he won at least 52, with his haul expected to grow significantly.

That left him with 750 delegates of the 1,144 needed for the nomination, compared with 260 for Santorum, 137 for Newt Gingrich and 75 for Ron Paul.

Santorum suspended his campaign two weeks ago rather than risk losing a primary in his home state of Pennsylvania.

Gingrich, too, seemed to be heading toward the sidelines, although he said he intends to complete his plans for several days of campaigning in North Carolina.